Quantum Mechanics in Chemistry

by Jack Simons and Jeff Nichols

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This is a text dealing with the basics of quantum mechanics and electronic structure theory. It provides an introduction to molecular spectroscopy and to the subject of molecular dynamics.

Description from LibreTexts.

Publisher
University of Utah
Subjects
Chemistry, Physical and Theoretical Chemistry Textbook Maps
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: The Basic Tools of Quantum Mechanics
  7. 1.1: Operators
  8. 1.2: Wavefunctions
  9. 1.3: The Schrödinger Equation
  10. 1.4: Free-Particle Motion in Two Dimensions
  11. 1.5: Particles in Boxes
  12. 1.6: One Electron Moving About a Nucleus
  13. 1.7: Harmonic Vibrational Motion
  14. 1.8: Rotational Motion for a Rigid Diatomic Molecule
  15. 1.9: The Physical Relevance of Wavefunctions, Operators and Eigenvalues
  16. 2: Approximation Methods
  17. 2.1: The Variational Method
  18. 2.2: Perturbation Theory
  19. 2.E: Approximation Methods (Exercises)
  20. 3: Nuclear Motion
  21. 3.1: The Born-Oppenheimer Separation of Electronic and Nuclear Motions
  22. 3.2: Time Scale Separation
  23. 3.3: Vibration/Rotation States for Each Electronic Surface
  24. 3.4: Rotation and Vibration of Diatomic Molecules
  25. 3.5: Separation of Vibration and Rotation
  26. 3.6: The Rigid Rotor and Harmonic Oscillator
  27. 3.7: The Morse Oscillator
  28. 3.8: Rotation of Polyatomic Molecules
  29. 3.9: Rotation of Linear Molecules
  30. 3.E: Exercises
  31. 3.10: Rotation of Non-Linear Molecules
  32. 3.11: Chapter Summary
  33. 4: Atomic Orbitals
  34. 4.1: Shapes of Atomic Orbitals
  35. 4.2: Directions of Atomic Orbitals
  36. 4.3: Sizes and Energies
  37. 5: Molecular Orbitals
  38. 5.1: Orbital Interaction Topology
  39. 5.2: Orbital Symmetry
  40. 5.3: Linear Molecules
  41. 5.4: Atoms
  42. 6: Quantum Mechanics in Reactions
  43. 6.1: Reduction in Symmetry Along Reaction Paths
  44. 6.2: Orbital Correlation Diagrams - Origins of the Woodward-Hoffmann Rules
  45. 7: Further Characterization of Molecular Orbitals
  46. 7.1: The LCAO-MO Expansion and the Orbital-Level Schrödinger Equation
  47. 7.2: Determining the Effective Potential
  48. 7.3: The Hückel Parameterization
  49. 7.4: The Extended Hückel Method
  50. 8: Electronic Configurations
  51. 8.1: Orbitals Do Not Provide the Complete Picture; Their Occupancy By the N Electrons Must Be Specified
  52. 8.2: Even N-Electron Configurations are Not Mother Nature's True Energy States
  53. 8.3: Mean-Field Models
  54. 8.4: Configuration Interaction (CI) Describes the Correct Electronic States
  55. 8.5: Summary
  56. 9: Symmetry of Electronic Wavefunctions
  57. 9.1: Electronic Configurations
  58. 9.2: Antisymmetric Wavefunctions
  59. 10: Angular Momentum and Group Symmetries of Electronic Wavefunctions
  60. 10.1: Angular Momentum Symmetry and Strategies for Angular Momentum Coupling
  61. 10.2: Electron Spin Angular Momentum
  62. 10.3: Coupling of Angular Momenta
  63. 10.4: Atomic Term Symbols and Wavefunctions
  64. 10.5: Atomic Configuration Wavefunctions
  65. 10.6: Inversion Symmetry
  66. 10.7: Review of Atomic Cases
  67. 11: Evaluating the Matrix Elements of N-electron Wavefunctions
  68. 11.1: Configuration State Functions can Express the Full N-Electron Wavefunction
  69. 11.2: The Slater-Condon Rules Give Expressions for the Operator Matrix Elements Among the CSFs
  70. 11.3: The Slater-Condon Rules
  71. 11.4: Examples of Applying the Slater-Condon Rules
  72. 11.S: Evaluating the Matrix Elements of N-electron Wavefunctions (Summary)
  73. 12: Quantum Mechanical Picture of Bond Making and Breaking Reactions
  74. 12.1: Concepts of Configuration and State Energies
  75. 12.2: Mixing of Covalent and Ionic Configurations
  76. 12.3: Various Types of Configuration Mixing
  77. 13: Molecular Rotation and Vibration
  78. 13.1: Rotational Motions of Rigid Molecules
  79. 13.2: Vibrational Motion Within the Harmonic Approximation
  80. 13.3: Anharmonicity
  81. 14: Time-dependent Quantum Dynamics
  82. 14.1: Time-Dependent Vector Potentials
  83. 14.2: Time-Dependent Perturbation Theory
  84. 14.3: Application to Electromagnetic Perturbations
  85. 14.4: The "Long-Wavelength" Approximation
  86. 14.5: The Kinetics of Photon Absorption and Emission
  87. 15: Spectroscopy
  88. 15.1: Rotational Transitions
  89. 15.2: Vibration-Rotation Transitions
  90. 15.3: Electronic-Vibration-Rotation Transitions
  91. 15.4: Time Correlation Function Expressions for Transition Rates
  92. 16: Collisions and Scattering
  93. 16.1: One Dimensional Scattering
  94. 16.2: Multichannel Problems
  95. 16.3: Classical Treatment of Nuclear Motion
  96. 16.4: Wavepackets
  97. 17: Higher Order Corrections to Electronic Structure
  98. 17.1: Orbitals, Configurations, and the Mean-Field Potential
  99. 17.2: Electron Correlation Requires Moving Beyond a Mean-Field Model
  100. 17.3: Moving from Qualitative to Quantitative Models
  101. 17.4: Atomic Units
  102. 18: Multiconfiguration Wavefunctions
  103. 18.1: Optimization of the Energy for a Multiconfiguration Wavefunction
  104. 18.2: The Single-Determinant Wavefunction
  105. 18.3: The Unrestricted Hartree-Fock Spin Impurity Problem
  106. 18.4: Atomic Orbital Basis Sets
  107. 18.5: The LCAO-MO Expansion
  108. 18.6: The Roothaan Matrix SCF Process
  109. 18.7: Observations on Orbitals and Orbital Energies
  110. 19: Multi-Determinant Wavefunctions
  111. 19.1: Introduction to Multi-Determinant Wavefunctions
  112. 19.2: Different Methods
  113. 19.3: Strengths and Weaknesses of Various Methods
  114. 19.4: Further Details on Implementing Multiconfigurational Methods
  115. 20: Response Theory
  116. 20.1: Calculations of Properties Other Than the Energy
  117. 20.2: Ab Initio, Semi-Empirical, and Empirical Force Field Methods
  118. 21: Problem Sets
  119. 22: Problems
  120. 22.1: The Basic Tools of Quantum Mechanics
  121. 22.1.1: i. Review Exercises
  122. 22.1.2: ii. Exercises
  123. 22.1.3: iii. Problems 1-10
  124. 22.1.4: iv. Problems 11-18
  125. 22.1.5: v. Review Exercise Solutions
  126. 22.1.6: vi. Exercise Solutions
  127. 22.2: Simple Molecular Orbital Theory
  128. 22.2.1: i. Review Exercises
  129. 22.2.2: ii. Exercises
  130. 22.2.3: iii. Problems
  131. 22.2.4: iv. Review Exercises Solutions
  132. 22.2.5: v. Exercise Solution
  133. 22.2.6: vi. Problem Solutions
  134. 22.3: Electronic Configurations, Term Symbols, and States
  135. 22.3.1: i. Review Exercises
  136. 22.3.2: ii. Exercises
  137. 22.3.3: iii. Problems
  138. 22.3.4: iv. Review Exercise Solutions
  139. 22.3.5: v. Exercise Solutions
  140. 22.3.6: vi. Problem Solutions
  141. 22.4: Molecular Rotation and Vibration
  142. 22.4.1: i. Exercises
  143. 22.4.2: ii. Problems
  144. 22.4.3: iii. Exercise Solutions
  145. 22.4.4: iv. Problem Solutions
  146. 22.5: Time Dependent Processes
  147. 22.5.1: i. Exercises
  148. 22.5.2: ii. Problems
  149. 22.5.3: iii. Exercise Solutions
  150. 22.5.4: iv. Problem Solutions
  151. 22.6: More Quantitative Aspects of Electronic Structure Calculations
  152. 22.6.1: i. Review Execises
  153. 22.6.2: i. Review Exercises-
  154. 22.6.3: ii. Exercises
  155. 22.6.4: iii. Problems
  156. 22.6.5: iv. Review Exercise Solutions
  157. 22.6.6: v. Exercise Solutions
  158. 22.6.7: vi. Problem Solutions
  159. Back Matter
  160. Index
  161. Glossary
  162. Detailed Licensing